Stick to their schedule. Nap time is vital, snacks are key and mom's big hugs when the bright lights and big noises get too much are what makes for bliss on board.
Snacks: Thank god for snacks, sometimes it is the only way to distract a jerk toddler who wants to bite and hit because he doesn't know he's hungry.
Nap Time: When we are on a cruise, nap time is a big deal because it lets my son rest, breastfeed and relax in the middle of his big adventure days.
Hugs: I can tell when my son is overstimulated and overwhelmed. Often that is the moment he needs a hug or some breastfeeding and a cuddle to reset his busy mind.
Games: The stairs on a cruise ship are great fun. I have carried my 33 pound dude up and down dozens and dozens of flights. But when he wants to walk it is a great and safe way to let him play. I like to show him the art on each landing, counting the interesting stairwells and jump and walk as we enjoy holding hands.